Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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15 views

Sum of the product of a cartesian product

I have two disjoint (though I suppose they don't need to be disjoint) sets, $M$ and $N$. I now want to take something like $$\sum_{(i,k) \in M\times N} i\cdot k$$ In english, I want a sum of the ...
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0answers
10 views

What is the geometric center and what is the other point?

In Euclidean geometry it is simple: In a triangle $\triangle ABC$ there is a single point $H_a$ on $BC$ such that the triangles $\triangle ABH_a$ and $\triangle ACH_a$ have the same area. the ...
1
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0answers
42 views

Is it “okay practice” to exclude the epicness from the definition of extremal / strong epis?

Basically I wonder, whether I "should" include the property of being epi in the definition of extremal epis / strong epis (/...) (dually for extremal monos etc.). One hand it is terminology-wise a ...
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0answers
7 views

Contour lines are synonyms for level curves. What is the “contour” synonym for level surfaces?

Contour lines are synonyms for level curves in 2 dimensional functions. What is the "contour" synonym for level surfaces in 3 dimensional functions?
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0answers
32 views

Is there a concept of distance between number of steps needed to move from one step to another?

Let's say that we have a set of rewrite rules: $$AB \mapsto AC, A \mapsto B, B \mapsto A$$ Given the two strings $ABC$ and $BCC$ we know we can rewrite $$ABC \mapsto ACC \mapsto BCC$$ We can ...
3
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0answers
51 views

Is there a name for this principle of logic? From $\exists a P(a), !bQ(b), \forall a(P(a) \rightarrow Q(a)),$ infer $\forall a(Q(a) \rightarrow P(a))$

In set theory, we have the following: Observation 0. Let $X$ denote a set. Let $A$ and $B$ denote subsets of $X$. Then if $A$ has at least one element, $B$ has at most one element, and $A ...
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1answer
27 views

What is the definition of a single valued function

this is potentially a dumb question but I am a touch confused about some terminology. I'm reading Ahlfor's complex analysis, and I am in a section on integrals of harmonic functions. I may be being ...
2
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0answers
16 views

Is there a name for smoothed maximum value function?

I have several arrays that look something like this: Spectrum Plot. Think gaussian curves, but shorter and with lots of noise. I've been comparing values for the sake of peak detection. Through ...
0
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1answer
15 views

Generic term for results of applying mathematical transformation to a value

Is there a generic way to refer to the summed values in this equation: I wanna say something like 'the result is the sum of three individual XXX XXX XXX performed on the percentile values', where ...
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0answers
20 views

Are scalar/vector fields basically just “multi-valued” functions?

Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead. From Wikipedia: a scalar field associates a scalar value to every point in a ...
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3answers
17 views

What does it mean for simple functions to have finite range

In Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics By Dan Simovici, Chabane Djeraba, it says: A simple function is a function $f: S \to \mathbb{R}$ that has finite ...
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1answer
16 views

Classes of exponent

I found this terminology in an a paper (link) and did not understand it's meaning. Here is the set of lines that I am talking about: For each prime $p \le g$, we remove all residue classes $\mod p$ ...
0
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1answer
25 views

What is the argument of the logarithm operator called?

In the expression $ln(y)$, what is '$y$' called. I'm asking for a noun analogous to exponent in $x^n$, where '$n$' is called the exponent. If I'm not mistaken, '$x$' in this case is the radix, or ...
1
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1answer
61 views

$\frac{d^{n}}{dt^{n}}$ meaning?

What is this called and what does it mean? $\frac{d^{n}}{dt^{n}}$ does it mean you differentiate an expression with respect to $t$, $n$ times? Is there a name for this? I want to do some research
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0answers
20 views

What does it mean that a function is determined by another?

What does it mean when a definition says that a function is "fully determined" or "uniquely determined" by another? For context, the sentence where I encountered the expression was the following ...
1
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0answers
37 views

Unsure of Probability Terminology

I am not sure how to call the following property (I have forgotten my probability theory!). I'd be grateful if someone can tell me the keywords: Suppose I have the following cartoon: I have a ...
1
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1answer
37 views

Maximal subcategory inside a multicategory

Let $\mathcal M$ be a multicategory. Let $C(\mathcal M)$ be a category consisting of all objects and all unary multimorphisms of $\mathcal M$. Is there a standard name for $C(\mathcal M)$?
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1answer
33 views

What is the name of the set obtained by multiplying a given number by any rational?

Given a number, is there a name for the set where each element results of multiplying this number by a rational? For a given $ n \in \mathbb N $: $$ \{ r \cdot n \mid r \in \mathbb Q \} $$
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0answers
8 views

Positive semi-definite vs. semi-positive definite?

I've heard and read the phrase positive semi-definite in many places. However, the only place I can recall seeing semi-positive definite is in my quantum mechanics text, John S. Townsend's ...
1
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1answer
43 views

Why is it called the *Inverse* Galois Problem?

This is just a very quick question and hopefully not poorly received. Question: Why is it called the inverse galois problem? The very brief statement given on wikipedia says Is every finite ...
-1
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0answers
38 views

Dream Function For Finding the Next Prime Following $n$

Is there any standard notation for this function, or is there not because it doesn't exist? If so, what is it? If not, let $D(n)$ be the dream function for finding the distance to the next prime ...
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2answers
52 views

How is the Net Change Theorem different from Fundamental Theorem Of Calculus II

1) Fundamental Theorem Of Calculus II $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ 2) Net Change Theorem $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ They are the same, why have two?
5
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4answers
605 views

Is my current understanding of the fundamental of calculus correct?

My current understanding: part 1) means essentially the integral is the inverse of the derivatve $$\frac {d}{dx} \int f'(x)dx = f'(x)$$ part 2) means essentially we can calculate the integral by ...
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5answers
64 views

Why do we not include $c$ in the computation of the definite integral?

Why is it when evaluating the definite integral we commonly opt to omit the constant $c$ $$\int_1^2x^2 \, dx= \left.\frac{x^3}{3} \right|_1^2 =\frac{2^3}{3}-\frac{1^3}{3}=\frac{7}{3}$$ But when ...
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0answers
35 views

Product of Cycles: Name to denote “direction” of composition

Is there a notation to denote the difference between these two products of cycles? It seems as though there are two conventions out there that should have a specific name for them. The subscripts for ...
2
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2answers
81 views

German combinatoric terms vs English terms

I'm a German Computer Science student and I currently work with combinatorics as part of my curriculum. I wanted to research combinatorics in English but I'm confused about the terminology. In German ...
2
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1answer
39 views

Why are left/right proper model categories called so?

A model category is called left proper if weak equivalences are preserved by pushouts along cofibrations, and right proper if they are preserved by pullbacks along fibrations. It is called proper if ...
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3answers
50 views

Is it correct to say all extrema happen at critical points but not all critical points are extrema?

Is it correct to say all extrema happen at critical points but not all critical points are extrema? This question is for single variable calculus. But it would be great if someone could also provide ...
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2answers
21 views

What is a bounded quantifier?

I was reading a Wikipedia article on arithmetical hierarchy and came across bounded quantifiers. I didn't know what those were and so quickly went to another article to read up on them and only became ...
0
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0answers
20 views

Proof strategy - How to prove this modeling of time series

The question is based on a paper titled : Forecasting high waters at Venice Lagoon using chaotic time series analysis and nonlinear neural networks On page 2 right above Eq(1), the authors say ...
3
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1answer
50 views

Do these graphs have names?

I'm working with finite, directed graphs equipped with a supplementary structure, consisting in a cyclic order on the edges meeting at a given vertex. This kind of graph seems ubiquitous when doing ...
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0answers
23 views

Ordinal numbers

I have a sequence of coefficients. I can obviously write "i-th" or "h-th coefficient", but I'm referring to the coefficient with number n-h. Can I write "(n-h)-th coefficient"?
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0answers
15 views

What is the scientific term for an analysis or comparison of percentage of two commodities?

My analysis has resulted in a graph where the x-axis is a percentage of one commodity and y-axis is the percentage of another commodity. Is there any concise name or terminology for this kind of ...
4
votes
1answer
45 views

Corollary **to** Theorem 1.2 or corollary **of** Theorem 1.2?

I think both ways are possible in English, but should I say This is a corollary to Theorem 1.2 or This is a corollary of Theorem 1.2 ?
1
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0answers
26 views

Partition-Generated Recurrence Relation

Suppose you have a series $\{A_n\}$ with the following recurrence relation: $$A_{n+1} = \sum_{\lambda(n)}\prod_{i=1}^{|\lambda|}A_{\lambda_i}$$ where $\lambda(n)$ is an integer partition of $n$ and ...
0
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1answer
34 views

Is it appropriate to refer to the “height” of a function?

I need to point out that a certain process will have an effect on the average "height" (i.e.: the average value of the function in the y axis) of a 1-dimensional function. Is it correct to say that ...
0
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1answer
24 views

Is a gradient system considered an ODE or PDE?

When you have a system of the type $$\dfrac{dx(t)}{dt} = \nabla V(x)$$ Is this considered an ODE or a PDE? Because you have a single derivative with respect to $t$ on the lefthand side, whereas on ...
2
votes
2answers
35 views

Is there a name for the way I am averaging the cost of cards?

My buddy and I were discussing different ways of deciding how much mana to include when constructing a deck. Without thinking much about it I used a method of finding the average converted mana cost ...
0
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0answers
27 views

Do global extrema of functions also happen on critical points?

Do global extrema of functions also happen on critical points? The wikipedia page says the theorem holds for all local extrema. But does it hold for globals too? Or are globals also considered locals ...
0
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1answer
43 views

What axiom in Math says “similar inputs should yield similar outputs”?

It is easy to take for granted the simple idea that similar input $x$ to a function $f(x)$ should yield similar outputs - such that if the difference between $x$ is arbitrary small, then we should ...
0
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0answers
19 views

Is it acceptable to call curves on parametric surfaces “isoparms”?

Let $\mathbf{r}(u,v):[a_0,b_0] \times [a_1,b_1] \to \mathbb{R}^3$ be a parametric surface. If $u$ and $v$ are fixed, is it allowed to call $\mathbf{r}(u,\cdot)$ and $\mathbf{r}(\cdot,v)$ "isoparms" or ...
1
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0answers
21 views

Does this partition of an indexed union have a standard name?

Let $\mathscr{I}$ be an arbitrary index set, and $\{A_i : i \in \mathscr{I}\}$ be a family of sets indexed on $\mathscr{I}$; $U = \bigcup_{i \in \mathscr{I}} A_i$; $\phi: U \to \{0, 1\}^\mathscr{I}, ...
0
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0answers
13 views

Name of this class of functions

How is a continuous and monotonic function called, that for a bounded input (e.g. $0..1$), generates results from $0..\infty$? As an example of where Im going: A similar class of functions, that goes ...
7
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2answers
158 views

Is there a name for an 'incomplete' factorial $\frac{n!}{m!}$?

I noticed I was computing $${n! \over m!} ,$$ where $n > m$, inefficiently, as $$\frac{\prod_{k=1}^{n} k}{\prod_{k=1}^m k},$$ when many terms cancel out and I could just be calculating ...
2
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1answer
42 views

Name of a particular category

I'd like to work with a certain category which seems classic to me, but I don't know its usual name. Let's define $$Ob(\mathcal{C}) = \{(Y,Y_1,Y_2,f) : Y = Y_1 \cup Y_2, f : Y_1 \to Y_2\},$$ where ...
1
vote
1answer
18 views

Permutation of rows with repetition

A binary matrix with exactly one entry of 1 in each row and 0s elsewhere performs a "permutation with repetition" of the rows of the matrix it left-multiplies. Example: $$ \begin{bmatrix} 1 & 0 ...
2
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1answer
29 views

What is the closure of $A = \{x| 1<\|x\|<3\} \cup \{(0,0)\}$ and why am I wrong?

Given $A = \{x| 1<\|x\|<3\} \cup \{(0,0)\}$ Find $\bar A$ My hunch is $\overline A = \{x| 1 \leq x \leq 3\} \cup \{0,0\}$, but my friend says I am wrong, the closure of $A$ must ...
3
votes
0answers
61 views

Is there a connection between the “independent sets” in matroids and “independent sets” in graph theory?

I've been reading up on matroids recently, which are used in the theory of greedy algorithms. A matroid is a pair $(X, I)$ where $X$ is a set and $I \subseteq \wp(X)$ is a family of sets over $X$ ...
0
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1answer
34 views

On “bounded” in intuition for a theorem involving autonomous 1st-order ODEs

Suppose we have an autonomous first-order ordinary differential equation $$\frac{dx}{dt} = f(x) \tag{*}$$ where $f$ is continuously differentiable for all $x \in D \subseteq \mathbb R$ s.t. the ODE ...
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1answer
64 views

$K$-monomorphism that is not $K$-automorphism?

I am confused by the terminology where $K$ precedes terms such as $K$-monomorphism and $K$-automorphism in Galois theory. I am trying to come up with a simple example about $K$-monomorphism that is ...